A mathematical model for the Fermi weak interactions

We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved

Design of a biologically inspired navigation system for the Psikharpax rodent robot

This work presents the development and implementation of a biologically inspired navigation system on the autonomous Psikharpax rodent robot. Our system comprises two independent navigation strategies: a taxon expert and a planning expert. The presented navigation system allows the robot to learn the optimal strategy in each situation, by relying upon a strategy selection mechanism

2-D non-periodic homogenization of the elastic wave equation: SH case

International audienceIn the Earth, seismic waves propagate through 3-D heterogeneities characterized by a large variety of scales, some of them much smaller than their minimum wavelength. The costs of computing the wavefield in such media using purely numerical methods, are very high. To lower them, and also to obtain a better geodynamical interpretation of tomographic images, we aim at calculating appropriate effective properties of heterogeneous and discontinuous media, by deriving convenient upscaling rules for the material properties and for the wave equation. To progress towards this goal we extend our successful work from 1-D to 2-D. We first apply the so-called homogenization method (based on a two-scale asymptotic expansion of the field variables) to model antiplane wave propagation in 2-D periodic media. These latter are characterized by short-scale variations of elastic properties, compared to the smallest wavelength of the wavefield. Seismograms are obtained using the 0th-order term of this asymptotic expansion, plus a partial first-order correction. Away from boundaries, they are in excellent agreement with solutions calculated at a much higher computational cost, using spectral elements simulations in the reference media. We then extend the homogenization of the wave equation, to 2-D non-periodic, deterministic media

1-D non periodic homogenization for the seismic wave equation

International audienceWhen considering numerical acoustic or elastic wave propagation in media containing small heterogeneities with respect to the minimum wavelength of the wavefield, being able to upscale physical properties (or homogenize them) is valuable mainly for two reasons. First, replacing the original discontinuous and very heterogeneous medium by a smooth and more simple one, is a judicious alternative to the necessary fine and difficult meshing of the original medium required by many wave equation solvers. Second, it helps to understand what properties of a medium are really ‘seen' by the wavefield propagating through, which is an important aspect in an inverse problem approach. This paper is an attempt of a pedagogical introduction to non- periodic homogenization in 1-D, allowing to find the effective wave equation and effective physical properties, of the elastodynamics equation in a highly heterogeneous medium. It can be extrapolated from 1-D to a higher space dimensions. This development can be seen as an extension of the classical two-scale homogenization theory applied to the elastic wave equation in periodic media, with this limitation that it does not hold beyond order 1 in the asymptotic expansion involved in the classical theory

Anisotropic self-affine properties of experimental fracture surfaces

The scaling properties of post-mortem fracture surfaces of brittle (silica glass), ductile (aluminum alloy) and quasi-brittle (mortar and wood) materials have been investigated. These surfaces, studied far from the initiation, were shown to be self-affine. However, the Hurst exponent measured along the crack direction is found to be different from the one measured along the propagation direction. More generally, a complete description of the scaling properties of these surfaces call for the use of the 2D height-height correlation function that involves three exponents zeta = 0.75, beta = 0.6 and z = 1.25 independent of the material considered as well as of the crack growth velocity. These exponents are shown to correspond to the roughness, growth and dynamic exponents respectively, as introduced in interface growth models. They are conjectured to be universal.Comment: 12 page

Nanoscale damage during fracture in silica glass

We report here atomic force microscopy experiments designed to uncover the nature of failure mechanisms occuring within the process zone at the tip of a crack propagating into a silica glass specimen under stress corrosion. The crack propagates through the growth and coalescence of nanoscale damage spots. This cavitation process is shown to be the key mechanism responsible for damage spreading within the process zone. The possible origin of the nucleation of cavities, as well as the implications on the selection of both the cavity size at coalescence and the process zone extension are finally discussed.Comment: 12 page

On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field

We consider a non-relativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. The system is translation invariant in the $x_3$-direction and we consider the reduced Hamiltonian $H(P_3)$ associated with the total momentum $P_3$ along the $x_3$-axis. For a fixed momentum $P_3$ sufficiently small, we prove that $H(P_3)$ has a ground state in the Fock representation if and only if $E'(P_3)=0$, where $P_3 \mapsto E'(P_3)$ is the derivative of the map $P_3 \mapsto E(P_3) = \inf \sigma (H(P_3))$. If $E'(P_3) \neq 0$, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant

Universal electric-field-driven resistive transition in narrow-gap Mott insulators

One of today's most exciting research frontier and challenge in condensed matter physics is known as Mottronics, whose goal is to incorporate strong correlation effects into the realm of electronics. In fact, taming the Mott insulator-to-metal transition (IMT), which is driven by strong electronic correlation effects, holds the promise of a commutation speed set by a quantum transition, and with negligible power dissipation. In this context, one possible route to control the Mott transition is to electrostatically dope the systems using strong dielectrics, in FET-like devices. Another possibility is through resistive switching, that is, to induce the insulator-to-metal transition by strong electric pulsing. This action brings the correlated system far from equilibrium, rendering the exact treatment of the problem a difficult challenge. Here, we show that existing theoretical predictions of the off-equilibrium manybody problem err by orders of magnitudes, when compared to experiments that we performed on three prototypical narrow gap Mott systems V2-xCrxO3, NiS2-xSex and GaTa4Se8, and which also demonstrate a striking universality of this Mott resistive transition (MRT). We then introduce and numerically study a model based on key theoretically known physical features of the Mott phenomenon in the Hubbard model. We find that our model predictions are in very good agreement with the observed universal MRT and with a non-trivial timedelay electric pulsing experiment, which we also report. Our study demonstrates that the MRT can be associated to a dynamically directed avalanche

Renewing accessible heptazine chemistry: 2,5,8-tris(3,5-diethyl-pyrazolyl)-heptazine, a new highly soluble heptazine derivative with exchangeable groups, and examples of newly derived heptazines and their physical chemistry

International audienceWe have prepared 2,5,8-tris(3,5-diethyl-pyrazolyl)-heptazine, the first highly soluble heptazine derivative possessing easily exchangeable leaving groups. We present its original synthesis employing mechanochemistry, along with a few examples of its versatile reactivity. It is, in particular, demonstrated that the pyrazolyl leaving groups can be replaced by several secondary or primary amino substituents or by three aryl-or benzyl-thiol substituents. In addition to being a synthetic platform, 2,5,8-tris(3,5-diethyl-pyrazolyl)-heptazine is fluorescent and electroactive, and its attractive properties, as well as those of the derived heptazines, are briefly presented

Modeling ASR Ambiguity for Dialogue State Tracking Using Word Confusion Networks

Spoken dialogue systems typically use a list of top-N ASR hypotheses for inferring the semantic meaning and tracking the state of the dialogue. However ASR graphs, such as confusion networks (confnets), provide a compact representation of a richer hypothesis space than a top-N ASR list. In this paper, we study the benefits of using confusion networks with a state-of-the-art neural dialogue state tracker (DST). We encode the 2-dimensional confnet into a 1-dimensional sequence of embeddings using an attentional confusion network encoder which can be used with any DST system. Our confnet encoder is plugged into the state-of-the-art 'Global-locally Self-Attentive Dialogue State Tacker' (GLAD) model for DST and obtains significant improvements in both accuracy and inference time compared to using top-N ASR hypotheses.Comment: Accepted at Interspeech-202